Browse > Article
http://dx.doi.org/10.11568/kjm.2016.24.4.751

MASS FORMULA OF SELF-DUAL CODES OVER GALOIS RINGS GR(p2, 2)  

Choi, Whan-hyuk (Department of Mathematics Kangwon National University)
Publication Information
Korean Journal of Mathematics / v.24, no.4, 2016 , pp. 751-764 More about this Journal
Abstract
We investigate the self-dual codes over Galois rings and determine the mass formula for self-dual codes over Galois rings $GR(p^2,2)$.
Keywords
codes over Galois ring; self-dual codes; mass formula;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 Jose Maria P. Balmaceda, Rowena Alma L. Betty, and Fidel R. Nemenzo, Mass formula for self-dual codes over ${\mathbb{Z}}_{p2}$, Discrete Mathematics 308 (14) (2008), 2984-3002.   DOI
2 A. R. Calderbank and N. J. A. Sloane, Modular and p-adic cyclic codes, Des. Codes Cryptography, 6 (1) (1995), 21-35.   DOI
3 Whan-Hyuk Choi, Kwang Ho Kim, and Sook Young Park, The classification of self-orthogonal codes over ${\mathbb{Z}}_{p2}$ of length ${\leq}3$, Korean Journal of Mathematics 22 (4) (2014), 725-742.   DOI
4 Philippe Gaborit, Mass formulas for self-dual codes over ${\mathbb{Z}}_4$ and ${\mathbb{F}}q +u{\mathbb{F}}_q$ rings, Information Theory IEEE Transactions on 42 (4) (1996) 1222-1228.   DOI
5 Fernando Q. Gouvea, p-adic Numbers, Springer, 1997.
6 Roger A. Hammons, Vijay P. Kumar, A. Robert Calderbank, N. Sloane, and Patrick Sole, The $Z_4$-linearity of Kerdock, Preparata, Goethals, and related codes, Information Theory IEEE Transactions on 40 (2) (1994), 301-319.   DOI
7 Jon-Lark Kim and Yoonjin Lee, Construction of MDS self-dual codes over Galois rings, Designs, Codes and Cryptography, 45 (2) (2007), 247-258.   DOI
8 Rudolf Lidl and Harald Niederreiter, Finite fields: Encyclopedia of mathematics and its applications, Computers & Mathematics with Applications 33 (7) (1997), 136-136.
9 Bernard R. McDonald, Finite rings with identity, volume 28. Marcel Dekker Incorporated, 1974.
10 Kiyoshi Nagata, Fidel Nemenzo, and Hideo Wada, Constructive algorithm of self-dual error-correcting codes In Proc. of 11th International Workshop on Algebraic and Combinatorial Coding Theory, pages 215-220, 2008.
11 Kiyoshi Nagata, Fidel Nemenzo, and Hideo Wada, The number of self-dual codes over ${\mathbb{Z}}_{p3}$, Designs, Codes and Cryptography 50 (3) (2009), 291-303.   DOI
12 Kiyoshi Nagata, Fidel Nemenzo, and Hideo Wada, Mass formula and structure of self-dual codes over ${\mathbb{Z}}_{2s}$, Designs, codes and cryptography 67 (3) (2013), 293-316.   DOI
13 Young Ho Park, The classification of self-dual modular codes, Finite Fields and Their Applications 17 (5) (2011), 442-460.   DOI
14 Vera Pless, The number of isotropic subspaces in a finite geometry Atti. Accad. Naz. Lincei Rendic 39 (1965), 418-421.
15 Vera Pless, On the uniqueness of the golay codes, Journal of Combinatorial theory 5 (3) (1968), 215-228.   DOI
16 Zhe-Xian Wan, Finite Fields And Galois Rings, World Scientific Publishing Co., Inc., 2011.